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We demonstrate a non-existence of exact equations for size N bigger then 4 and propose appropriate approximations, the quality of which is studied in examples obtained within Markov chains framework.\n  We derive several exact formulas describing properties of the automaton, in"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1208.5886","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CG","submitted_at":"2012-08-29T11:51:39Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP","nlin.SI","physics.geo-ph"],"title_canon_sha256":"1289f2b8743dc056bddb04ae9128a4c5810f477cc957b4e6a1e160411c0c7d01","abstract_canon_sha256":"43d1398e2b860f5c6b3516215c9bd5c9fba50d91d817bb7ac4f234819613d90f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:48.402118Z","signature_b64":"tvyG7C+Dq4OR1QMC/jdd+XSVnwL1FWBtLgGTAO8evejYbSdByVGwoSDXYFimvnWiSu0VR42ilUjo8J0e8g6fDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29a3706011545530bf10c1d8461ee61f12f08370fbc229b8a1229e80500bd66c","last_reissued_at":"2026-05-18T03:46:48.401286Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:48.401286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite Random Domino Automaton","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","nlin.SI","physics.geo-ph"],"primary_cat":"nlin.CG","authors_text":"Mariusz Bialecki","submitted_at":"2012-08-29T11:51:39Z","abstract_excerpt":"Finite version of Random Domino Automaton (FRDA) - recently proposed a toy model of earthquakes - is investigated. 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